An analytical approach to the study of extraordinary transmission and fishnet metamaterials
- Autores: Vicente Jesús Delgado Pozo
- Directores de la Tesis: Ricardo Marqués Sillero (dir. tes.), Lukas Jelinek (codir. tes.)
- Lectura: En la Universidad de Sevilla ( España ) en 2013
- Idioma: inglés
- Títulos paralelos:
- Una aproximación analítica al estudio de metamateriales de transmisión extraordinaria
- Tribunal Calificador de la Tesis: Javier Martí Sendra (presid.), Francisco Luis Mesa Ledesma (secret.), Miguel Beruete Díaz (voc.), Francisco Medina Mena (voc.), Mário Gonçalo Silveirinha (voc.)
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- Resumen
Metamaterials are commonly defined as artificial materials with physical properties not found in nature. The special properties of these materials relies in their tailored structures which usually consist in a host medium with periodic or randomly distributed inclusions. Most metamaterials are electromagnetic metamaterials (EMM), with inclusions that interact with electromagnetic waves and acquire electric and/or magnetic moments.
When the spacing or periodicity of the constitutive elements is at least one order of magnitude smaller than the wavelength of electromagnetic waves interacting with the medium, it makes sense to talk about effective electric permittivity and magnetic permeability characterizing the metamaterial. We say that the medium is homogenizable.
In 1968, V. G. Veselago studied theoretically the peculiar electromagnetic properties of an hypothetical medium with simultaneously negative electric permittivity and magnetic permeability. In such materials there would be backward propagation (with group and phase velocity pointing to opposite directions), inverse Doppler and Vavilov-Cerenkov effects and negative Goos-Hanchen.
The research and design of EMM has been encouraged in the last decade since J. B. Pendry demonstrated theoretically that a slab with electric permittivity and magnetic permeability (that is, equal in absolute value to those of free space but with opposite sign) has the capability of restoring evanescent waves components coming from a source point into an image point located at a distance that is twice the thickness of the slab.
The basic design method to achieve artificially negative permittivity values is the wire medium design. The parallel wire medium, with all the wired oriented in the same direction, behaves as an effective uniaxial dielectric with negative permittivity along the direction of the wires in the long wavelength limit. Three dimensional connected wire mediums behave as isotropic effective medium with negative permittivity.
Effective negative permeability is achieved with the so called Split Ring Resonators (SRRs). SRRs consist in a capacitive loaded closed metallic loop. Thanks to the capacitor, the SRRs acquires high negative polarizabilities that yield negative magnetic permeability. Different designs have been proposed for SRRs: edge-coupled SRR, broadside-coupled SRR or the double-split SRR. An alternative to SRRs, and also a limiting case of the double-split SRR are the cut-wire pair.
Despite the enthusiasm in the last years, negative index metamaterials have severe restriction. They are frequency dispersive and negative parameters can be obtained in relatively narrow frequency bands; the fabrication of double-negative metamaterials (i.e. the combination of negative permittivity and permeability structures with wires and SRRs for example) is complicated specially at high frequencies and finally losses in metals at optical frequencies limit the functionality of SRRs or cut-wire pairs.
An alternative that overcomes the problems of losses and integration of both negative permittivity and permeability systems are the fishnet metamaterials that can be described as stacks of periodically perforated screens. In fact, each of the screens in the stack can be viewed as the superposition of a cut-pair wire (in the direction of the applied magnetic field) and long wires in the direction of the applied electric field. Fishnet metamaterials are being currently investigated as possible media to build invisibility cloaks or super-resolution lenses and much effort has been devoted to calculate its effective electromagnetic parameters.
Individual screens also exhibit a recently discovered phenomenon called Extraordinary Optical Transmission (EOT). When an opaque screen with a periodic distribution of slits, holes or other defects is illuminated by an electromagnetic wave with a wavelength close to the periodicity of the defects, a peak of unexpected enhanced transmission, respect to the background transmission at other close frequencies, appears. This phenomenon was first discovered at optical frequencies by Thomas Ebbesen et al. in 1998 in a silver screen with a periodic array of cylindrical holes and was called Extraordinary Optical Transmission (EOT). Standard diffraction theory can not explain the amplitude of the peaks. The excitation of surface plasmons (collective oscillations of electrons) at the interface between the metal, with negative real part of permittivity, and air was first argued as physical background of the phenomenon. However, Extraordinary Transmission (ET) has also been found in metals at microwave frequencies or dielectrics, in which cases real part of permittivity tends to infinity or is positive and surface plasmons do not exist.
EOT is a current topic of intensive research due to its potential applications in photonic circuits, optical sensing in biomedicine or fabrication of left-handed metamaterials. The physical background behind ET is an issue of controversy. Different theories have tried to explain the phenomenon from different perspectives. Channeling of surface plasmons (SPs) excited at the metal-air/dielectric interface were first claimed to be the origin of the enhanced transmission. However, ET has been reported in cases where SPs can not exist such as dielectric screens or metallic screens at microwave frequencies.
In this work, we provide different analytical models for the characterization of ET and electromagnetic propagation in fishnets at microwave, terahertz or optical frequencies. All of the models are based on waveguide analysis and in the surface impedance concept, and allow for a rapid electromagnetic characterization of the structures. The success of the models can be measured in terms of the accuracy of the results and CPU time of its computations compared to full wave simulation carried out with a commercial electromagnetic simulator.
Next, we briefly summarize the contents of the different chapters in which the thesis is divided -In chapter 0 we will present the main ET and fishnet structures that will be analyzed through the thesis.
-In chapter 1 the basic theory behind our models for the characterization of EOT and fishnets will be exposed. The problem of an incident plane wave on an EOT screen will be reduced to its unit cell. Waveguide analysis will be employed to calculate the electromagnetic fields at both sides of the screen and inside the apertures, that may consist in slits (1D configurations) or holes (2D configurations), in terms of Bloch modes. Rigorous mode-matching or coupled-wave analysis would require to compute also the electromagnetic fields inside the penetrable screen. However, in that case the numerical models are not practical. In chapter 1, we will also introduce the surface impedance concept in the context of EOT. Surface impedance approximation will reduce the complexity of the numerical problem making it affordable.
-In chapter 2 the theory described in chapter 1 will be applied to EOT screens with small slits or holes under normal incidence. In the small slits/holes approximation, variations of the different modes in the cross section of the apertures will be neglected. The model will be particularized with specific approximations or modifications to metallic screens at optical frequencies, dielectric screens and corrugated surfaces.
-In chapter 3 the waveguide and surface impedance model will be extended to the case of oblique incidence and slits or holes of any size. In this case there appear additional transmission peaks with frequencies that depend on the angle of incidence and polarization of the incident wave.
-In chapter 4 the small holes approximation will be extended to infinite stacks of EOT screens (fishnets). Dispersion diagrams of the fishnets at normal incidence will be obtained confirming the existence of backward bands.
-In chapter 5 the waveguide and surface impedance model will be applied to dielectric loaded EOT screens and stacks with a finite or infinite number of screens. In finite stacks the refraction of a Gaussian beam will be studied confirming the existence of negative refraction in case of TM polarization. In infinite stacks, the dispersion diagrams for any angle of incidence and the iso-frequency contours will be obtained. The connection between EOT and fishnets and the intermediate regime between them will also be investigated.
